Wildlife Diseases

CRITIQUE OF CWD MODELS

Chronic wasting disease in deer and elk: a critique of current models and
their application

Eric M. Schauber and Alan Woolf

Authors' address: Cooperative Wildlife Research Laboratory and Department of
Zoology, Southern Illinois University, Carbondale, IL 62901, USA; e-mail for
Schauber: schauber@siu.edu.

Abstract

Chronic wasting disease (CWD), a fatal transmissible spongiform
encephalopathy of deer
(Odocoileus spp.) and elk (Cervus elaphus), presents a challenge to wildlife
managers
because little is known about its transmission, yet it could severely
threaten wildlife popu-lations if action is not taken rapidly. Published
mathematical models predict that CWD
could devastate populations of free-living deer and elk, prompting wildlife
managers to
attempt large-scale eradication of deer in hopes of containing CWD
outbreaks. Our objective
is to critically examine the theoretical and empirical support for current
models of
CWD epizootiology, in light of herd health-management actions. We identify a
critical,
untested premise (i.e., strictly frequency-dependent transmission) that
underlies the dire
model predictions. We re-evaluate published comparisons of model output with
field data
and find little support for published model structures. Given the
uncertainty surrounding
the future effects of chronic wasting disease on deer and elk populations,
and the potential
costs of unnecessarily culling large numbers of charismatic and valuable
animals, we propose
that consideration of alternative models and management actions in a
decision-theoretic
framework is necessary for wildlife management actions to retain their
scientific basis.

Chronic wasting disease (CWD) has recently emerged as a major concern of
wildlife managers,
biologists, and stakeholders throughout North America (Enserink 2001,
Williams et al. 2002).
Chronic wasting disease is a fatal transmissible spongiform encephalopathy
(TSE; Williams and
Young 1980) that has been observed in free-living and captive deer
(Odocoileus spp.) and elk (Cervus elaphus) and is the only TSE known to
persist in free-living wildlife populations (Spraker et al. 1997, Miller et
al. 2000). Although CWD appears to have persisted for decades at relatively
low prevalence in an enzootic region in parts of Colorado and Wyoming,
recent data suggest that its prevalence in free-living mule deer (O.
hemionus) and elk may be increasing (Miller et al. 2000, Gross and Miller
2001). Outside this enzootic area, CWD has been detected in free-living mule
deer, white-tailed deer (O. virginianus), or elk in Illinois, Nebraska, New
Mexico, Saskatchewan, South Dakota, and Wisconsin and appears to be
spreading (Williams et al. 2002). No link between CWD and disease in humans
or noncervid livestock has been found, but these risks cannot be dismissed
with absolute certainty (Bartz et al. 1998, Raymond et al. 2000, Hamir et
al. 2001). Compounding the potential impact on wildlife and human health,
CWD threatens to erode favorable public perception of wildlife resources and
the fundamental importance of sport hunting as both a tool for management of
free-ranging deer and elk populations and a major monetary source for
wildlife management agencies and local economies.

While much is known about the empirical epizootiology of CWD (Williams et
al. 2002), critical parameters and processes related to modes and patterns
of transmission are unknown. Also, CWD epi-zootics in wild herds have not
been observed long enough to know what their ultimate population-level
effects will be. Therefore, mathematical models are critical tools for
assessing the potential impact of CWD on deer and elk populations and
weighing this risk against the costs of alternative management actions.
Mathematical models have been developed to synthesize existing knowledge of
CWD epizootiology in wild mule deer; these models uniformly predict that CWD
can cause extinction of host populations (Miller et al. 2000, Gross and
Miller 2001). In the face of dire model predictions, scarce data, and
uncertainty, experts have recommended strong and rapid steps to contain and
eradicate CWD outbreaks (Gross and Miller 2001, Williams et al. 2002). The
Wisconsin Department of Natural Resources has begun an attempted eradication
of all white-tailed deer with-in a >900-km 2 area where CWD has been
detected (Nolen 2002), representing a prominent management philosophy and a
strategy likely to be consid-ered by many agencies responsible for managing
populations at risk for CWD.

We believe it useful to critically examine the premises and empirical
support of published CWD models. While we acknowledge that rapid management
action to control CWD may be warranted and that wildlife managers invariably
must act without the luxury of complete knowledge, we propose that
science-based wildlife management will advance if competing models and
management alternatives are carefully explored in a decision-theoretic
framework. All scientific knowledge is tentative and provisional, and
science advances by repeatedly confronting hypotheses and models with logic
and data. It is in this spirit that we offer the following critique of the
premises and support of current CWD models.

Theoretical foundation

A model is a formal construct that illuminates the logical consequences of
the assumptions upon
which it is based, and the validity of the model as a representation of
reality depends on how closely its assumptions reflect the characteristics
of the real system. The published models of CWD epizootiology in wild mule
deer (Miller et al. 2000, Gross and Miller 2001) share a common assumption:
the number of effective contacts between an infectious individual and other
individuals per unit time (ß) is constant and independent of population size
or density. This premise results in frequency-dependent transmission, where
the force of transmission is a function of the frequency (i.e., proportion)
of infectious individuals within the population (Appendix A). The idea of
frequency-dependent transmission is based on the premise that opportunities
for contact between an infectious individual and susceptible individuals are
unaffected by population size (de Jong et al. 1995). An important
distinction exists between population size and density, depending on the
scale over which transmission occurs. For example, if transmission occurs
exclusively within social groups and the number of individuals per group is
constant, changes in the number of groups inhabiting an area will change the
population density on a large scale but may not affect the local density or
contact rate experienced by an individual within a group. The assumption of
frequency-dependent transmission for CWD has been justified on the basis of
the aggregative, migratory,
and habitat-selection behaviors of wild deer (Gross and Miller 2001), but
its importance to
model output has not been discussed.

Epidemiological theory indicates that pure frequency-dependent transmission
strongly promotes unstable host-pathogen dynamics (Getz and Pickering 1983),
such that the disease either dies away (ß<ß*, where ß* is a threshold value)
or drives the host and itself to extinction (ß>ß*). However, if ß is not
constant but decreases as the host density decreases, known as
density-dependent transmission, the disease and its host can reach a stable
equilibrium or exhibit regular cycles (Anderson and May 1978, May and
Anderson 1978). The presumption of frequency-dependent versus
density-dependent transmission is critical to the predicted outcome of an
epizootic: host-pathogen extinction versus host-pathogen coexistence. Gross
and Miller (2001:213) report "a disturbing result of this modeling exercise
was our inability to identify a set of realistic parameters that permits
sustained coexistence of CWD in a wild deer population." We emphasize that
this dire outcome of CWD models is entirely a predictable consequence of the
frequency-dependent assumption and does not stem from any particular known
characteristics of CWD.
 

Whether transmission is frequency-dependent or density-dependent is
determined by the primary
mechanism of transmission and the spatial structure of host populations.
Frequency-dependent
transmission is particularly likely in cases of venereal or vector-borne
transmission (May and
Anderson 1978, Getz and Pickering 1983) because the number of mates per
individual host or host-bites per vector may be essentially independent of
host density in many species. Frequency-depend-ent transmission also is
promoted when a host population is subdivided into groups of nearly constant
size, so that changes in overall population size or density do not affect
the local density within groups (de Jong et al. 1995). Due to their
matrilineal social structure (Hawkins and Klimstra 1970; Geist 1981, 1982;
Nelson and Mech 1999), deer and elk appear to be candidates for
frequency-dependent transmission. However, the CWD agent is most likely
transmitted via bodily fluids both through direct contact and indirectly
because the agent appears to persist in the environment (Miller et al.
1998). We argue that this combination of direct and indirect transmission is
unlikely to be strictly frequency-dependent. Also, mule deer and elk
(particularly
females) congregate on winter range (Geist 1982, 1998), where the exudates
of an infected animal potentially can contact a larger number of animals if
more animals congregate in or migrate
along the same area, suggesting that some form of density-dependent
transmission is feasible. Group
size and social structure of deer and elk also respond to changes in
population density (Kie and
Bowyer 1999, Hebblewhite and Pletscher 2002). Finally, if CWD transmission
is strictly frequency-dependent, other diseases of deer or elk transmitted
by the oral-fecal route should exhibit similar
dynamics and should cause host extinction. This has not been observed.

Classical epidemiological models have been based on the premise that ß is
directly proportional to the population density of hosts (Kermack and
McKendrick 1927, Anderson and May 1978), and such strictly linear
density-dependence is clearly unrealistic for wild deer and elk. However, it
also is unrealistic to presume that ß is completely independent of host
density. For example, CWD has become much more prevalent in captive cervid
herds maintained at high densities than in free-living herds (Williams and
Young 1980,Williams et al. 2002), suggesting that population density has a
positive influence on the probability of transmission. For group-living
species like cervids, ß may be approximately constant over a range of
moderate population densities but is likely to change when population
density is very low or high. Thus, ß might rise to an asymptote as
population density increases (Dietz 1982, Heesterbeek and Metz 1983,
Antonovics et al. 1995, Heesterbeek and Roberts 1995, Ramsey et al. 2002) or
could vary as a power function or some other nonlinear function of density
(Figure 1). Incorporating these nonlinear forms of density-dependent
transmission into the model of Miller et al. (2000) would result in
persistent host-pathogen coexistence if ß drops below ß * as host density
drops. Output of CWD models is very sensitive to changes in the value of ß
(Miller et al. 2000, Gross and Miller 2001), so even weakly
density-dependent transmission may enable host-pathogen coexistence. The
many unknown aspects of CWD transmission prohibit robust prediction of the
population impact.

Figure 1. (Not shown) Plausible relationships between host population
density and the number of effective contacts per unit time between each host
individual and others. Current published models of chronic wasting disease
assume no relationship (constant), whereas Anderson-May type models assume a
linear relationship. However, there exists a range of intermediate and more
complex relationships that are biologically feasible.

Empirical support

Miller et al. (2000) tested the validity of their frequency-dependent model
by comparing its predictions with empirical data relating to changes in CWD
prevalence over time and patterns of CWD prevalence across sex and age
classes in mule deer in Colorado. However, the apparent concordance
reported by Miller et al. (2000) between observed and predicted CWD
prevalence across age-sex
classes is in error. As the model is described by Miller et al. (2000), it
is incapable of producing a pattern in which infection prevalence differs
across age classes >4 years old or between sexes (Appendix B). This
contrasts with their field data and their purported model output (Miller et
al. 2000: figure 4). The empirical age-prevalence relationship of CWD in
free-living mule deer, particularly its rarity in older male deer, cannot be
explained by the model and indicates that some important biological
processes are missing from the model.

The concordance with empirical data also is questionable for the model of
Gross and Miller (2001), who used the same age-prevalence data for mule deer
as Miller et al. (2000) but lumped the data between sexes. The authors
claimed that the nearly flat age-prevalence relationship that emerged from
the model "closely matched independent field observations," (Gross and
Miller 2001:210) despite the prominent differences in observed CWD
prevalence among age groups. Prevalence of CWD, averaged across age classes,
was similar in model output and field data, but whether that similarity
truly represents concordance with independent data is unclear. In the model
of Gross and Miller (2001), CWD prevalence generally increased over time
during simulation runs, so the model output would closely match observed CWD
prevalence only at certain time steps. The authors neglect to indicate from
what time step in the simulation the model output came and whether that time
step was chosen based on criteria other than similarity to observed data.

Implications for management

Culling has been used often in attempts to contain or eliminate wildlife
diseases by driving host
populations below a threshold density (Barlow 1996, Wobeser 2002). However,
unlike density-dependent transmission, strict frequency-dependent
transmission does not permit the existence of a
threshold host density below which the pathogen cannot persist (Getz and
Pickering 1983).
Therefore, incomplete host eradication (i.e., partial culling) can
deterministically cause elimination of a disease with density-dependent but
not a frequency-dependent transmission, unless infected individuals can be
identified and culled selectively (Gross and Miller 2001). If transmission
is truly frequency-dependent, incomplete eradication might only hasten the
ultimate extinction of that host population without preventing disease
spread to other populations. In other words, even if the frequency-dependent
assumption upon which eradication programs are based is true, it implies
that eradication is unlikely to successfully control the spread of the
disease unless nearly 100% of hosts are eliminated.

Given that the assumption of strict frequency-dependent transmission is both
critically important and untested, it seems prudent to consider what
management options might be appropriate if this assumption is untrue. If
transmission is not fre-quency-dependent, then a threshold host density may
exist. If so, that threshold host density may be high or low, relative to
current densities of deer and elk. If the threshold density is high, the
disease will not substantially reduce wild populations, and CWD does not
endanger deer herds. If it is low, the host population must be reduced to
even lower densities to locally eliminate the disease. It remains an open
question whether such extreme culling programs will be logistically or
politically feasible, particularly if CWD introduction is not a one-time
occurrence or the CWD agent persists in the environment. Complete
elimination of CWD from all North American deer and elk herds is unlikely,
despite the best efforts of humans, suggesting that it could be reintroduced
relatively frequently into disease-free populations (because both CWD
epidemiology and proposed management actions occur on the scale of decades,
"relatively frequently" might mean once per 20 years). If CWD introduction
in a region is not a one-time occurrence, then CWD establishment could be
prevented in the long term only by suppressing host densities for an
indefinite period below the densities that would result if the disease took
its course. Even if necessary and successful, defeating CWD via host
eradication would come at a cost, not only economic but also in terms of
public perception of wildlife resources, acceptance of management paradigms,
and interruption of the hunting tradition. These costs of success and the
uncertainty surrounding the necessity of host eradication should be
accounted for when weighing alternative management actions.

We do not intend to imply that any attempt to manage wildlife diseases by
reducing host density  is wrong or undesirable. However, the fact that all
wildlife diseases are not intensively managed
implies that managers implicitly weigh the costs of various actions against
the risks of inaction. For CWD, models are the best available tools for
estimating the risks of inaction and therefore the
appropriate magnitude of response. The existence of a model of CWD
epizootiology that predicts cer-tain extinction of the host could be
interpreted as justification for whatever management action is
deemed most likely to prevent this dire outcome. However, any modeler with
understanding of fun-damental ecological theory and no consideration for
validity of assumptions could produce models
predicting certain extinction of one or all species for any host-pathogen
(Getz and Pickering 1983), host-parasite (Hassell and May 1973),
predator-prey (Murdoch and Oaten 1975), or other ecological interaction.
Therefore, predictions of alternative models need to be considered and
judged on the validity of their assumptions and concordance with data in
order to evaluate the appropriate magnitude of response. Our objective is to
call attention to a critical untested premise (i.e., frequency-dependent
transmission) of current CWD models and to temper acceptance of model
predictions with the uncertainty surrounding the validity of that premise
and the weakness of empirical support. Gross and Miller (2001:213) claimed
that "to the extent that modeled mechanisms of CWD transmission appear to
offer at least a reasonable approximation of disease processes occurring in
nature, it follows that this model provides plausible forecasts of future
epidemic trends." We agree with the logic of the first part of this
statement but question whether theory or data permit the acceptance of these
models as a reasonable approximation of CWD transmission
dynamics. The predictions of frequency-dependent models of CWD epizootiology
(Miller et al. 2000, Gross and Miller 2001) represent a small set of
possible outcomes of CWD epizootics in wild
populations. Other outcomes are also plausible, and their actuality depends
on the true (but
unknown) relationships between transmission and population density, sex and
age structure, and spa-tial structure. Current frequency-dependent models
are consistent with the observed long-term per-sistence of CWD at low
prevalence in free-living deer and elk, but this observation also is
consistent with other hypotheses (e.g., CWD will remain at relatively low
prevalence indefinitely). The range of possible reality states and the
potential benefits and costs of alternative management actions may be best
analyzed in a decision-theoretic framework where potential costs of inaction
and alternative actions are explicitly weighed and point to the urgent need
for research into the transmission dynamics of CWD to firmly base management
decisions on the best possible science.

Acknowledgments. Preparation of this manuscript was supported by the
Illinois Department of
Natural Resources. We thank P. Shelton, J. Roseberry, and two anonymous
reviewers for comments
that substantially improved earlier drafts of this manuscript.

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Eric M. Schauber (photo) is a wildlife ecologist with the Cooperative
Wildlife Research Laboratory (CWRL) and an assistant professor in the
Department of Zoology at Southern Illinois University Carbondale (SIUC). He
obtained a B.S. in wildlife from University of Massachusetts-Amherst, an
M.S. in wildlife from Oregon State University, and a Ph.D. in ecology from
University of Connecticut. Eric's research has focused on epi-zootiology,
ecotoxicology, population dynamics, and predator-
prey interactions of small mammals, with an emphasis on quantitative methods
and modeling. Alan Woolf is the director of the CWRL and a professor in the
Department of Zoology at SIUC. He obtained a B.S. from Cornell University,
an M.S. from Colorado State University, and returned to Cornell for his
Ph.D. His research interests are varied, although wildlife disease has been
a major component. He has served the CWRL for the past 23 years and has been
director since 1987.

Associate editor: Krausman

Appendix A

If the number of effective contacts per individual per year (ß) is constant
and population size (N) is a finite integer, then the probability of an
uninfected host becoming infected during a time step (i.e., force of
infection) is given by 1 -(1 -1/N)Iß, where I is the number of infectious
hosts (McCarty and Miller 1998, Miller et al. 2000; note typographical error
in Gross and Miller 2001:208). As N approaches infinity (e.g., if a large
geographic area is examined) but infection prevalence (1/N) remains
constant, this probability converges to the zero term of a Poisson
distribution subtracted from unity: 1 -exp(-ß I/N). Numerical analyses
indicate that the finite-N and Poisson transmission probabilities differ by
a factor of ~0.05 or less for N>10. Thus, the force of transmission is
primarily a function of infection prevalence and not the absolute of
number of infecteds. For time steps <1 year, as steps (and hence ß ) become
small, the Poisson
probability converges to ß I/N.

Appendix B

Model output reported in figure 4C-D in Miller et al. (2000) cannot be
produced by the model they
describe; see figure 4 in Gross and Miller (2001) for an age-prevalence
relationship consistent with model structure. Below, we describe the model
of Miller et al. (2000), which represents the spread of CWD in a free-living
population of mule deer and prove that their model necessarily produces
sex-and age-independent prevalence for above age class 4. Gross and Miller
(2001) use a slight modification of the same model structure.

Yearly survival of uninfected yearling and adult deer is assumed to differ
between sexes but not age classes (except that no deer survives past age
class 15), and the probability of a susceptible deer becoming infected in a
given year is equal for all sex and age classes except fawns (which may
receive vertical transmission from their mothers). After a deer is infected,
it spends 1 year in the latent stage before becoming infectious. After an
animal becomes infectious, survival is successively halved in each of 3
subsequent years  irrespective of sex and age. No infectious deer are
allowed to live >3 years in this model. For each sex the number of infected
individuals in age class j >4 in year t (I t,j ) is a function of the number
of uninfected individuals in age class j -4 in year t -4 (S t-4 , j-4 ), the
sex-specif-ic yearly survival rate (sex ), and the yearly probabilities of
becoming infected for the previous 4 years (P t-4 , P t-3 , P t-2 , P t-1 ):

The total number of individuals of that sex in age class j >4 in year t (N
t,j ) is given by the sum of I t,j and those individuals that were
uninfected in year t-4, avoided infection entirely, and survived for 4
years:

The product S t-4, j-4 ×(sex ) 4 can be factored out of both I t,j and N t,j
, so infection prevalence (I t,j /N t,j ) is function only of P t-4 , P t-3
, P t-2 , and P t-1 , which are constant across sex and age classes. We
conclude that, given the assumptions upon which this model is based,
infection prevalence cannot differ between sexes or among age classes above
age class 4.